Structural Results for General Partition, Equistable and Triangle graphs

Miklavič and Milanič (2011) introduced the connections among the classes of equistable, general partition and triangle graphs. We present results concerning the three classes aforementioned. In particular, we show that the general partition and triangle classes are both closed under the operations of substitution, induction and contraction of modules. Moreover, we show that the triangle condition is sufficient for a planar graph to be a general partition graph, providing a generalisation of a result by Mahadev, Peled and Sun (1994) on equistable outerplanar graphs.